Perimeter of a Composite Figure worksheet - Free Printable

Problem: Calculate the perimeter of each composite figure.

#### Steps to Success:
1. Read and highlight the given information.
2. Observe the diagram and count & label the number of sides.
3. Find the missing side(s).
4. Write the formula for the perimeter: \( P = \text{Sum of All Sides} \).
5. Check to ensure all sides are added correctly.

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Figure 1:

#### Given:
- Dimensions: 8 cm, 10 cm, 7 cm, 5 cm, 3 cm
- Missing side: The horizontal segment at the bottom.

#### Solution:
1. Identify the missing side:
- The total horizontal length is 8 cm.
- The known horizontal segments are 3 cm and 5 cm.
- Missing horizontal side = \( 8 - (3 + 5) = 0 \) cm (This indicates no additional horizontal segment is needed).

2. Calculate the perimeter:
- Perimeter = Sum of all sides
- Perimeter = \( 8 + 10 + 7 + 5 + 3 + 7 = 40 \) cm

#### Answer:
\[ \boxed{40} \]

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Figure 2:

#### Given:
- Dimensions: 12 cm, 9 cm, 7 cm, 8 cm
- Missing side: The vertical segment on the right.

#### Solution:
1. Identify the missing side:
- The total vertical length is 9 cm.
- The known vertical segments are 7 cm and 2 cm (since \( 9 - 7 = 2 \)).
- Missing vertical side = 2 cm.

2. Calculate the perimeter:
- Perimeter = Sum of all sides
- Perimeter = \( 12 + 9 + 7 + 8 + 2 + 2 = 40 \) cm

#### Answer:
\[ \boxed{40} \]

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Figure 3:

#### Given:
- Dimensions: 60 mm, 15 mm, 40 mm, 30 mm
- Missing side: The horizontal segment at the bottom.

#### Solution:
1. Identify the missing side:
- The total horizontal length is 60 mm.
- The known horizontal segments are 40 mm and 30 mm.
- Missing horizontal side = \( 60 - (40 + 30) = -10 \) mm (This indicates no additional horizontal segment is needed).

2. Calculate the perimeter:
- Perimeter = Sum of all sides
- Perimeter = \( 60 + 15 + 40 + 30 + 15 + 15 = 175 \) mm

#### Answer:
\[ \boxed{175} \]

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Figure 4:

#### Given:
- Dimensions: 7½ m, 4 m, 2 m, 1½ m
- Missing side: The horizontal segment at the bottom.

#### Solution:
1. Identify the missing side:
- The total horizontal length is 7½ m.
- The known horizontal segments are 4 m and 2 m.
- Missing horizontal side = \( 7.5 - (4 + 2) = 1.5 \) m.

2. Calculate the perimeter:
- Perimeter = Sum of all sides
- Perimeter = \( 7.5 + 4 + 2 + 1.5 + 1.5 + 1.5 = 18 \) m

#### Answer:
\[ \boxed{18} \]

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Final Answers:

1. \( \boxed{40} \)
2. \( \boxed{40} \)
3. \( \boxed{175} \)
4. \( \boxed{18} \)